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We discuss the critical points of the functional Ｆλ, μ (J, g) = ∫M (λτ+μτ* )dvg on the spaces of all almost Hermitian structures АН(M) with (λ,μ) ∈ R2 - (0,0),where τ and τ* being the scalar curvature and the *-scalar curvature of (J, g), respectively. We shall give several characterizations of Kähler structure for some special classes of almost Hermitian manifolds, in terms of the critical points of the functionals Fλ,μ(J,g) on АН(M). Further, we provide the almost Hermitian analogy of the Hilbert's result.
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참고문헌 (11)
참고문헌 신청
A. Gray / 1976 / Curvature identities for Hermitian and almost Hermitian manifolds / Tohoku Math. J. 28 (4) : 601 ~ 612
A. Gray / 1976 / The structure of nearly Kahler manifolds / Math. Ann. 223 (3) : 233 ~ 248
A. Gray / 1980 / The sixteen classes of almost Hermitian manifolds and their linear invariants / Ann. Mat. Pura Appl. 123 : 35 ~ 58
D. E. Blair / 1986 / Critical associated metrics on symplectic manifolds. in: Nonlinear problems in geometry / Amer. Math. Soc. : 23 ~ 29
D. Hilbert / 1915 / Die Grundlagen der Physik / Nachr. Ges. Wiss. Goott. : 395 ~ 407
A. Gray / 1976 / The structure of nearly Kahler manifolds / Math. Ann. 223 (3) : 233 ~ 248
A. Gray / 1980 / The sixteen classes of almost Hermitian manifolds and their linear invariants / Ann. Mat. Pura Appl. 123 : 35 ~ 58
D. E. Blair / 1986 / Critical associated metrics on symplectic manifolds. in: Nonlinear problems in geometry / Amer. Math. Soc. : 23 ~ 29
D. Hilbert / 1915 / Die Grundlagen der Physik / Nachr. Ges. Wiss. Goott. : 395 ~ 407
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